Convolution of a discrete continuous function for reconstruction

Question

From chapter 9 page 198 of https://github.com/t4world/Computer-Graphics/blob/master/Fundamentals-of-Computer-Graphics-Fourth-Edition.pdf

I am confused as to what this book's description is saying exactly:

As with discrete convolution, we can put bounds on the sum if we know the filter’s radius, $r$, eliminating all points where the difference between $x$ and $i$ is at least $r$:

The error comes from this sum

They say that points at $x-r$ being integer are discarded from the sum, of which they are not if the ceiling takes them in. This must be an error and it has been confusing me for so long now.

Answer 1

The statement is:

eliminating all points where the difference between $x$ and $i$ is at least $r$

so eliminate those points for which

$$ |x - i | \gt r \tag{1}$$

Isn't that correct? One could argue whether the words say

$$ |x - i | \ge r $$

instead, which might be problematic at the border, but using (1) the statement seems OK to me.

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The text after the equation says:

Note, that if a point falls exactly at distance $r$ from $x$ (i.e., if $x − r$ turns out to be an integer), it will be left out of the sum.
This is in contrast to the discrete case, where we included the point at $i − r$.

So the discrete case includes it the boundary but the continuous case doesn't.